三元DNA Golay码的构造

摘要

Golay code is a fairly good linear code and one of the only two perfect codes reaching the Ham-ming periphery. In recent years, DNA encoding, as a research hotspot of error-correction code, enjoys some updated and better properties than traditional encoding,and is also the key problem in DNA compu-ting, thus reasonable DNA coding could improve the reliability and stability of experiment and ensure the successful rate of DNA computation. Obviously,the construction of DNA codes by using traditional codes is of significant importance. How to construct ternary DNA Golay codes D12 and D11 by using ternary Golay codes G12 and G11 is described and the properties of these two ternary DNA Golay codes are also given in this paper.%Golay码是一类比较好的线性码，并且是仅有的两类达到Hamming界的完全码中的一类。而DNA编码是近几年纠错码界研究的热点，且比传统纠错码具有更新更好的一些性质。它是DNA计算中的重点和难点问题，且是核心问题，所以合理的DNA编码可以提高实验的稳定性和正确性，从而确保DNA计算的成功率。所以，用传统纠错码构造DNA纠错码是一项有意义的工作。本文给出了利用三元Golay码G12和G11构造三元DNA Golay 码D12和D11的方法，并给出了这两种三元DNA Golay码的性质。